A note on homogeneous bent functions

Bent functions are used to build blocks for cryptographically strong S-boxes and spread spectrum systems. The concept of semi bent functions and quarter bent functions is presented. Based on the new concept, an approach to construct bent functions is proposed. A simpler method to find all 30 homogeneous bent functions of degree 3 in 6 Boolean variables, which were previously discovered by a computer search, is given. It is proved that there do not exist homogeneous bent functions of degree m in 2 m Boolean variables for m > 3, without invoicing results from the difference set theory.